# Arithmetic mean

### Arithmetic Mean

The arithmetic mean of a set of numbers (or variables) is the sum of all the numbers, divided by the number of numbers - the average of the set. If we let ${AM}$ denote Arithmetic Mean,

$AM=\frac{x_1+x_2+\cdots+x_n}{n}$

is the arithmetic mean of the $\displaystyle {n}$ numbers $\displaystyle x_1,x_2,\ldots,x_n$.

For example, if I wanted to find the average of the numbers 3, 1, 4, 1, and 5, I would compute:

$\frac{3+1+4+1+5}{5} = \frac{14}{5}.$

Arithmetic means show up frequently in contest problems, often in the AM-GM inequality or its variant, the RMS-AM-GM-HM inequality.